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st: Cornfield and Woolf confused? -cc- vs -exactcc- vs Breslow&Day


From   "Michel Camus" <Michel_Camus@hc-sc.gc.ca>
To   statalist@hsphsun2.harvard.edu
Subject   st: Cornfield and Woolf confused? -cc- vs -exactcc- vs Breslow&Day
Date   Mon, 2 Dec 2002 09:51:34 -0500

Stata's -cc- and Dupont & Plummer's -exactcc- do not provide the same
Cornfield confidence intervals for ORs.
Moreover, Stata's -cci- does not provide the same results as those by
Breslow & Day (Stat.Methods in Cancer Research-Vol.1, p.124, 135-6)
neither. Why is it so? Is their a mistake in Stata's -cci- ?
Stata:
. cci 96 104 109 666 , cornfield
                         Proportion
                 |   Exposed   Unexposed  |     Total     Exposed
-----------------+------------------------+----------------------
           Cases |        96         104  |       200      0.4800
        Controls |       109         666  |       775      0.1406
-----------------+------------------------+----------------------
           Total         205         770  |       975      0.2103
                 |      Point estimate    |  [95% Conf. Interval]
                 |------------------------+----------------------
      Odds ratio |         5.640085       |  4.003217     7.94673
(Cornfield)
      Odds ratio |         5.640085       |  4.000589     7.95147  (Woolf)
      Odds ratio |         5.640085       |  3.937435     8.06179  (exact)
                 +-----------------------------------------------
Breslow & Day:
The CLs given by B&D are: 3.94 - 8.07 (Cornfield),
                          4.00 - 7.95 (Woolf).
Dupont & Plummer:
Those given by -exactcci- are:
                 |      Point estimate    |  [95% Conf. Interval]
                 |------------------------+----------------------
                 |                        | Cornfield's limits
      Odds ratio |         5.640085       |  3.942972    8.071281  Adjusted
                 |                        |  3.937435    8.061794
Unadjusted
                 |                        | Exact limits
                 |                        |  3.937467    8.061784
                                            Woolf's limits
      Odds ratio |         5.640085       |  4.000589    7.951467  (Woolf)

All 3 sources agree on Woolf.
However, Stata's -cci- is much too close to Woolf's CI and much too far
from the "exact CI".
Is there an error?
As to the difference between -exactcc- and -cc- regarding exact limits,
-cc- calls "exact" what -exactcci- terms "Unadjusted Cornfield's limits",
while B&D and D&P seem to agree on Cornfield's "adjusted" CLs. Why does
Stata's -cc- results seem ... "odd"?
What am I missing? (... other than a proper statistical training!)

Michel Camus, epidemiologist
Health Canada


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